Answers
[tex]csc(-x)-1~~ = ~~\cfrac{cos^2(x)}{csc(-x)+1} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{cos^2(x)}{csc(-x)+1}\implies \cfrac{1-sin^2(x)}{\frac{1}{sin(-x)+1}}\implies \cfrac{1-sin^2(x)}{\frac{1}{-sin(x)+1}}\implies \cfrac{[1-sin(x)][1+sin(x)]}{ ~~ \frac{-1+sin(x)}{sin(x)} ~~ } \\\\\\\ [1-sin(x)][1+sin(x)]\cdot \cfrac{sin(x)}{-1+sin(x)} \\\\\\\ [1-sin(x)][1+sin(x)]\cdot \cfrac{sin(x)}{-[1-sin(x)]} \\\\\\\ [1+sin(x)][-sin(x)] \implies \boxed{-sin(x)-sin^2(x)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]csc(-x)-1\implies \cfrac{1}{sin(-x)}-1\implies \cfrac{1}{-sin(x)}-1\implies \boxed{\cfrac{-1-sin(x)}{sin(x)}}[/tex]
now, as you can see is a no dice, before doing many simplifications, I often check them graphically, so I know what's cooking, anyhow, Check the picture below, they are definitely not the same, the red one is the one on the right-hand-side.
Related Questions
find the missing length indicated
Answers
Using Pythagoras theorem, we can find the length of the missing side to be 10 units.
Define Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, also referred to as the Pythagorean theorem.
The Pythagorean Theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of its other two sides.
In the given triangle, the base is given as:
b = 6 units.
height, h = 8 units.
Let the missing side be = x.
Now as per the Pythagoras theorem,
x² = 8² + 6²
⇒ x² = 64 + 36
⇒ x² = 100
⇒ x = 10.
Therefore, the length of the missing side of the triangle here is 10 units.
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A $40,000 car depreciates in value at a rate of 36% per year. The
value, V, after t years can be modeled by the function V =
40,000(0.64). Which function is equivalent to the original function?
. V = 40,000(0.8)St
V=40,000(0.8)2t
V = 40,000(0.8)
V = 40,000(0.8)
Answers
The correct function equivalent to the original function V = 40,000(0.64) is V = 40,000(0.64)ⁿ.
What is percent?Percent is a way of expressing a fraction or a decimal as a fraction of 100. It is denoted by the symbol "%". For example, the fraction 3/4 can be written as 75% and the decimal 0.5 can be written as 50%. Percentages are commonly used in everyday life to express values such as discounts, interest rates, and success rates.
Here,
The original function V = 40,000(0.64) models the value, V, of a $40,000 car after t years, where the car depreciates at a rate of 36% per year. The expression 0.64 represents the remaining value of the car after one year, which is obtained by subtracting 36% from 100% (i.e., 100% - 36% = 64%).
To find an equivalent function, we need to simplify 0.64. We can write 0.64 as 0.8², since 0.8 multiplied by itself gives 0.64.
So, V = 40,000(0.64) is equivalent to V = 40,000(0.8²), which simplifies to V = 40,000(0.64). This means that both expressions represent the same function that models the value of the car after t years, given that the car depreciates at a rate of 36% per year.
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For what values of x does the graph of f(x) have a horizontal tangent? (Enter your answers as a comma-separated list.)
f(x) = x³ + 7x² + x + 1
X=
Answers
The point in which f(x) have a horizontal tangent are (-7 + √46)/3, (-7 - √46)/3
What values of x does f(x) have a horizontal tangentTo find the values of x where the graph of f(x) has a horizontal tangent, we need to find where the derivative of f(x) is equal to zero (since the derivative gives the slope of the tangent line).
First, we find the derivative of f(x):
f'(x) = 3x² + 14x + 1
Next, we set f'(x) equal to zero and solve for x:
3x² + 14x + 1 = 0
Using the quadratic formula, we get:
x = (-14 ± √(14² - 431)) / (2*3)
x = (-14 ± √(184)) / 6
x = (-14 ± 2√46) / 6
Simplifying:
x = (-7 ± √46) / 3
Therefore, the values of x where the graph of f(x) has a horizontal tangent are (-7 + √46)/3 and (-7 - √46)/3.
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You and your four friends buy tickets to a baseball game. The total cost is $70. Write and solve an equation to find the total cost of each ticket.
Answers
Answer: 14 dollars.
Step-by-step explanation:
You (1) + your four friends (4) is 5.
5 times a number is 70.
5x=70
70/5=14
x=14
On a farm there are 600 animals distributed in two areas. Of the 600 animals, 4/6 are in zone A and the rest in zone B.
What part of the animals is in zone b?
How many animals are there in each part?
Answers
Answer:
[tex]A=\frac{4}{6} *600 = 400\\B=\frac{2}{6} *600 = 200[/tex]
math how much is 37.4x2.2= ?
Answers
Answer:
82.28
this was really easy,
What is Jane's hourly rate? * (1 Point) HAMBURGER PALACE ENTERPRISES, INC. PAYROLL ENDING 3/14/09 NAME JANE BROWN EMPLOYEE NO. L4325 EARNINGS Description Hrs. Amount Tax Regular CURRENT YTD 20 120.00 120.00 1650.00 CHECK NO. 9343 Medicare AMOUNT $87.50 TAXES WITHHELD Fed Income Tax Social Sec State Income Tax Current YTD Description 12.72 174.90 MEALS 7.44 102.30 1.74 3.60 23.93 OTHER DEDUCTIONS 49.50 Amount 7.00
Answers
So, Jane's hourly rate is $6.00 per hour.
What is division?In mathematics, division is a basic arithmetic operation that involves splitting a number or quantity into equal parts or groups. It is the inverse operation of multiplication, where we find out how many times one number (the divisor) can fit into another number (the dividend) without leaving any remainder.
Here,
However, we can calculate her hourly rate by dividing her total earnings by the number of hours she worked.
From the payroll information provided, Jane earned $120.00 for 20 hours of work. Therefore, her hourly rate would be:
Hourly rate = Total earnings / Number of hours worked
Hourly rate = $120.00 / 20 hours
Hourly rate = $6.00 per hour
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In the United States, 41% of 18 to 29-year-olds said in a survey held in March 2020 that they turrently subscribed to Hulu. What is the probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu?
Answers
The probability in a random sample of 55 18 to 29-year-olds that 20 will say they currently have a subscription to Hulu is: 0.087.
How to find the probability?This is a binomial distribution problem, where n = 55 and the probability of success (i.e. a person subscribing to Hulu) is p = 0.41.
The probability mass function of a binomial distribution is:
P(X = x) = (nCx) * p^x * (1-p)^(n-x)
where nCx is the binomial coefficient (i.e. the number of ways to choose x items from n items).
So, in this case, we want to find P(X = 20):
P(X = 20) = (55C20) * 0.41^20 * (1-0.41)^(55-20)
P(X = 20) ≈ 0.087
Therefore, the probability that in a random sample of 55 18 to 29-year-olds, 20 will say they currently have a subscription to Hulu is approximately 0.087or 8.7%.
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consider the function.
f(x)= √x
g(x)= √x-3+1
h(x)= √x+1-2
which statement compares the relative locations of the minimums of the functions?
Answers
The correct statement regarding the relative minimums of each function is given as follows:
The minimum of h(x) is farther left and down from the minimums of f(x) and g(x).
What are the relative minimums of each function?The function f(x) is defined as follows:
f(x)= √x.
It has a relative minimum at (0,0), which is one the first quadrant.
The function g(x) is defined as follows:
√x-3+1
It is a translation of 3 units right and 1 unit up of f(x), hence the minimum has coordinates (3,1), which is on the first quadrant.
The function h(x) is defined as follows:
h(x)= √x+1-2
It is a translation of 1 unit left and 2 units down of f(x), hence the minimum has coordinates (-1, -2), which is on the third quadrant.
The third quadrant is farther left and down from the first quadrant.
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Use the given information to find the unknown value.
2. y varies
1. y varies directly as the square root
inversely with the cube of x.
of x. When x = 16, then y = 4. Find y
y = 1. Find y when x = 1.
when x = 36.
When x = 3, then
3. The distances that an object falls varies directly with the
square of the time, t, of the fall. If an object falls 16 feet in one
second, how long for it to fall 144 feet?
4. The rate of vibration of a string under constant tension varies
inversely with the length of the string. If a string is 24 inches long
and vibrates 128 times per second, what is the length of a string
that vibrates 64 times per second?
Answers
Applying the definition of variation, we have:
1. When x = 36, y = 6.
2. When x = 1, y = 27.
3. It takes 3 seconds for the object to fall 144 feet.
4. Length of a string that vibrates 64 times per second is 48 inches.
What is an Inverse Variation?Inverse variation is a type of relationship between two variables in which one variable increases while the other decreases, or vice versa, in a way that the product of the two variables remains constant.
In other words, if we have two variables x and y that are inversely proportional, we can write:
x × y = k, where k is a constant.
1. We are given that y varies directly as the square root of x. This means that we can write:
y = k√x
where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 16, y = 4:
4 = k√16
4 = 4k
k = 1
Now we can use this value of k to find y when x = 36:
y = 1√36
y = 6
Therefore, when x = 36, y = 6.
2. We are given that y varies inversely with the cube of x. This means that we can write:
y = k/x³
where k is a constant of proportionality. To find the value of k, we can use the given information that when x = 3, y = 1:
1 = k/3³
1 = k/27
k = 27
Now we can use this value of k to find y when x = 1:
y = 27/1³
y = 27
Therefore, when x = 1, y = 27.
3. We are given that the distance that an object falls varies directly with the square of the time, t, of the fall. This means that we can write:
d = kt²
where d is the distance, k is a constant of proportionality, and t is the time. To find the value of k, we can use the given information that when t = 1, d = 16:
16 = k(1)²
16 = k
k = 16
Now we can use this value of k to find the time it takes for the object to fall 144 feet:
144 = 16t²
9 = t²
t = 3
Therefore, it takes 3 seconds for the object to fall 144 feet.
4. We are given that the rate of vibration of a string under constant tension varies inversely with the length of the string. This means that we can write:
r = k/L
where r is the rate of vibration, L is the length of the string, and k is a constant of proportionality.
To find the value of k, we can use the given information that when L = 24 inches, r = 128 vibrations per second:
128 = k/24
k = 3072
Now we can use this value of k to find the length of a string that vibrates 64 times per second:
64 = 3072/L
L = 48 inches
Therefore, the length of a string that vibrates 64 times per second is 48 inches.
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Suppose that buses are scheduled to arrive at a bus stop at noon but they are always X minutes late, where X is an exponential random variable with a mean of 4 minutes. Suppose that you arrived at the bus stop precisely at noon, and have been waiting for 10 minutes. Compute the probability that you have to wait an additional six minutes or more.
Answers
On solving the provided question, we can say that Given that you have already waited for 10 minutes, the inequality that you will have to wait another six minutes or longer is around 0.0183.
What is inequality?A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.
Applying the exponential distribution's memoryless characteristic, we have:
P(Y ≥ 6 | Y > 10) = P(Y ≥ 16)
= 1 - P(Y < 16)
= 1 - F(16) (16)
where F(t) is the exponential distribution's cumulative distribution function (CDF) with a mean of 4 minutes.
F(t) = 1 - e(-t/) yields the CDF of an exponential distribution with mean, where t 0. As a result, we have:
[tex]P(Y \geq 6 | Y > 10) = 1 - F(16) (16)\\= 1 - (1 - e^(-16/4))\\= e^(-4) (-4)\\≈ 0.0183[/tex]
Given that you have already waited for 10 minutes, the likelihood that you will have to wait another six minutes or longer is around 0.0183.
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6.177×10 to the 4th power
Answers
Answer:
61,770
Step-by-step explanation:
6.177 x [tex]10^{4}[/tex]
[tex]10^{4}[/tex] = 10,000
6.177 x 10,000 = 61,770
So, the answer is 61,770
Write an equation for a rational function with the given characteristics.
Vertical Asymptotes at x= -2 and x=4, x-intercepts at (-4,0) and (2,0), horizontal asymptote at y= -3.
Enclose numerators and denominators in parentheses. For example (a-b)/(1+n).
Include a multiplication sign between symbols. For example, a*x.
F(x) =
Answers
An equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4).
Explain about the rational function?Any function that can be expressed as a polynomial divided by such a polynomial is said to be rational. The domain of either a rational function is just the set of all numbers besides the zeros of the denominator since polynomials are specified everywhere.As x = -2 and X = 4 have vertical asymptotes, the denominator will contain the equations (x+2) and (x-4)
The terms (x+4) and 1 will be in the numerator since the x intercepts are (-4,0) , respectively (x-0).
Our current formula is f(X) = a(x+4)(x) / (x+2)(x-4)
We examine the horizontal asymptote to determine the value of A.
The limit of a function as x -> infinity would be - 3 since the horizontal asymptote reflects what the function looks like as x approaches infinity.
Thus, an equation for a rational function with the given characteristics is found as: f(X) = a(x+4)(x) / (x+2)(x-4)
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help im doing the math diagnostic
Answers
Answer: -5 1/4
Step-by-step explanation:
After answering the final question incorrectly, Sandra's score will be -5 1/4 in fraction form, and -5.25 in decimal form. This is because every time Sandra gets a question wrong her grade goes down by -3/4 points. And -4 1/2 minus -3/4 is -5 1/4. I hope this helped. If not, let me know and I can try to reword it.
Answer: b
Step-by-step explanation:
Rafael wants to find the slope of the line
Answers
The mistake that Rafael made is interchanging the y-values with the x-values.
The real slope of the line is 25.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope (m) = (100 - 50)/(4 - 2)
Slope, m = 50/2
Slope, m = 25.
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Find the equation of the exponential function represented by the table below
Answers
We can cοnclude that the expοnential functiοn represented by the given table is [tex]y = 3(0.5)^x[/tex]
What is Expοnential Functiοn?An expοnential functiοn is a mathematical functiοn οf the fοrm [tex]f(x) = ab^x[/tex], where a and b are cοnstants and b is greater than 0 and nοt equal tο 1. It is a type οf mathematical mοdel that describes a prοcess where a quantity grοws οr decays at a rate prοpοrtiοnal tο its current value οver time οr space.
An expοnential functiοn has the fοrm:
[tex]\mathrm y = ab^x[/tex]
where "a" is the initial value οf the functiοn, and "b" is the grοwth factοr οr base οf the functiοn.
Tο find the equatiοn οf the expοnential functiοn represented by the given table, we can use the first twο data pοints tο determine the values οf "a" and "b", and then check if the remaining data pοints fit the functiοn.
Using the first data pοint (0, 3), we get:
[tex]3 = ab^0[/tex]
3 = a
Using the secοnd data pοint (1, 1.5), we get:
[tex]1.5 = ab^1[/tex]
1.5 = 3b
b = 0.5
Therefοre, the equatiοn οf the expοnential functiοn represented by the given table is:
[tex]y = 3(0.5)^x[/tex]
We can check the remaining data pοints tο see if they fit the functiοn:
Fοr [tex]x = 2, y = 3(0.5)^2 = 0.75[/tex]
Fοr[tex]x = 3, y = 3(0.5)^3 = 0.375[/tex]
Since all the data pοints fit the equatiοn, we can cοnclude that the expοnential functiοn represented by the given table is:
[tex]y = 3(0.5)^x[/tex]
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A rectangle has an area of 60 square inches and the length is 4 inches more than the width. Find the length and width of the rectangle
Answers
Answer:
w = 6in, l = 10in
Step-by-step explanation:
Area of a rectangle is [tex]A=l*w[/tex]
and [tex]l = 4 + w[/tex]
We can solve for length and width by substituting these values for the equation.
[tex]60in^2=(4+w)*w[/tex]
[tex]60in^2=4w+w^2[/tex]
[tex]0 = w^2 + 4w + 60in^2[/tex]
factor out the equation.
[tex]0= (w+10)(w-6)[/tex]
therefore w = 6in (tossing out the negative solution)
which means
[tex]l = 4 + w[/tex]
[tex]l = 6in + 4[/tex]
l = [tex]10in[/tex]
Hope this helps!
Brainliest is much appreciated!
The following chart shows the number of rows in an auditorium and the total number of seats. Find an equation that defines the number of seats with respect to the number of rows
Answers
Answer:
Step-by-step explanation:
[tex]S=40R+20[/tex]
PLS 100PTS
WILL MARK AS BRAINLIEST
a ladder 20m long, leaning against a vertical wall makes an angle of 40⁰ with the horizontal ground. with the aid of a sketch diagram, determine the distance of the foot of the ladder from the wall (write your answer to 2 decimal places)
Answers
To determine the distance of the foot of the ladder from the wall, we can use trigonometry. Let's call the distance we want to find "x".
First, let's draw a diagram:
|\
| \
20 | \ x
| \
|____\
40°
In this diagram, the ladder is the hypotenuse of a right triangle, and the distance we want to find ("x") is one of the legs. The other leg is the height of the ladder on the wall, which we don't need to know in order to solve the problem.
We can use the trigonometric function for the sine of an angle to relate the angle of elevation to the distance "x" and the length of the ladder:
sin(40°) = x / 20
To solve for "x", we can multiply both sides by 20:
20 sin(40°) = x
Using a calculator, we can evaluate the sine of 40 degrees to get:
20 sin(40°) ≈ 12.85
So the distance of the foot of the ladder from the wall is approximately 12.85 meters, rounded to two decimal places.
Which of the following is the number 316.72 written in scientific notation?
A.
B. 3.1672 × 10²
C.
3.1672 x 10-2
D.
3.1672 x 103
3.1672 10
E. 3.1672 × 10-³
Answers
We can rewrite 3.1672 × 10¹² as 3.1672 × 10² The correct option is A
How to write a number in scientific notation ?First we first express it as a number between 1 and 10 multiplied by a power of 10. In this case, 316.72 can be expressed as:
3.1672 × 10¹² (since we move the decimal point 2 places to the right to get to 31672)
However, in scientific notation, the exponent should represent the number of places the decimal point is moved. Since we moved the decimal point to the right, the exponent should be negative.
Therefore, we can rewrite 3.1672 × 10¹² as:
3.1672 × 10²
So, the answer is (A).
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2. The graph of f(x) = -x² +8x+ 20 is sketched below. The graph intersects the x-axis at (-2;0) and (10;0), and the y — axis at (0; 20). The point (4;36) is the turning point of f. -2 20 0 Y (4:36) 1 10 the a is called th T
Answers
In this case, the equation is -x^2 + 8x + p = 0. Comparing this to the standard quadratic equation ax^2 + bx + c = 0, we can see that a = -1, b = 8, and c = p.
To find the discriminant, we can substitute these values into the formula:
b^2 - 4ac = 8^2 - 4(-1)(p) = 64 + 4p
We want this expression to be equal to zero, so we can set it equal to zero and solve for p:
64 + 4p = 0
4p = -64
p = -16
Therefore, the value of p for which -x^2 + 8x + p = 0 has equal roots is -16.
Quick Math Answer ok
Answers
Circumference
A quadrilateral with vertices at A(4,-4), B(4, -16), C(12, -16), and D(12,-4) has been dilated with a center at the origin.
The image of D, point D', has coordinates (36, -12). What is the scale factor of the dilation?
ㅇㅎ
9
O 3
O 3
09
Answers
Answer:
the scale factor = 3
Step-by-step explanation:
the question is basically saying: how did (12,-4) jump to (36,-12)
we can make d represent the scale factor used to get (12,-4) to (36,-12)
so,
12d = 36
-4d = -12
all there's left to do is to simply solve for d, which is 3
i-ready an 80-ounce bottle of apple juice contains 32 ounces of water what percent of the bottle of apple juice is wayer
Answers
The percent of the bottle of apple juice is 40%.
What is a percentage, and how is it different from a fraction or a decimal?An element of a whole number is a fraction. There are many different kinds of fractions. Three-quarters, for instance, is a fraction.
A decimal point separates a fractional component from an integral component to form a decimal. In the decimal 2.5, for instance, the fractional portion comes after the decimal point and is followed by the integer 2, which is put before it.
Per cent simply means one in a hundred. Hence, it is a number with a fractional representation that has a denominator of 100. As a result, fractions of a whole number are also described using percentages.
Given that, 80-ounce bottle of apple juice contains 32 ounces of water.
Thus,
% of water = (32 / 80) * 100 = 40%
Hence, the percent of the bottle of apple juice is 40%.
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QUICK, ANSWER THIS QUESTION FOR 30 POINTS!!!!
Answers
help me please this hard
Answers
Answer: -1/2
Step-by-step explanation:
To find the slope: rise/run
starting from the point (0,2), you go up 1 to reach the line
Therefore 1 is your rise.
Then go right 2 units and you hit the line again.
Therefore the slope is 1/2.
But the linear line is going downwards, so it is a negative slope
Therefore your final answer is:
-1/2
Let U={2,3,4,5,6,7,8,9,10,11), A = {3,5,7,9,11}and B = {7,8,9,10,11}. Use this information to answer the following questions
A-B
(A-B)^c
U-(A-B)^c
(AUB)^c
(A^cUB^c)^c
Answers
Using set theory, the element in each of the set are, A - B = {3, 5}, (A - B)^c = {2, 4, 6, 7, 8, 9, 10, 11}, U - (A - B)^c = {3, 5}, (A \cup B)^c = {2, 4, 6} and (A^c U B^c)^c = {7, 9, 11}.
What is the element in each set?The given sets are:
U = {2,3,4,5,6,7,8,9,10,11}
A = {3,5,7,9,11}
B = {7,8,9,10,11}
We can use these sets to find the following:
1. A - B: The elements in set A that are not in set B are {3, 5}.
2. (A - B)^c: The complement of set A - B in U contains all the elements in U that are not in A - B. These elements are {2, 4, 6, 7, 8, 9, 10, 11}.
3. U - (A - B)^c: This set contains all the elements in U that are not in the complement of A - B. These elements are {3, 5}.
4. (A U B)^c: This set contains all the elements in U that are not in the union of sets A and B. The union of A and B is {3, 5, 7, 8, 9, 10, 11}, so the complement is {2, 4, 6}.
5. (A^c U B^c)^c: This set contains all the elements in U that are in neither the complement of set A nor the complement of set B. The complement of set A is {2, 4, 6, 8, 10} and the complement of set B is {2, 3, 4, 5, 6}. The union of these two sets is {2, 3, 4, 5, 6, 8, 10}, so the complement of this set in U is {7, 9, 11}.
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Alice walks along a road which can be modeled by the equation y=4x, where (0,0) represents her starting point. When she reaches a certain point A, she turns right, so that she is traveling perpendicular to the original road, until she stops at the point (85,0).
Answers
Therefore , the solution of the given problem of equation comes out to be spot A's coordinates are (80,-20).
Equation: What is it?In mathematical formulas, it is common to use the same variable term to guarantee agreement between two claims. Mathematical assertions, also known as equations expression, are employed to convey the equality of numerous academic figures. In this case, the normalise method adds b + 6 using the data of y + 6 rather than splitting 12 into two parts.
Here,
Let (a,b) represent the location of point A. Consequently, the inclination of the line through (0,0) and (a,b) is
=> m = (b - 0) / (a - 0) Equals b / a
This line being parallel to the initial road gives us:
=> m = -1/4
Therefore:
=> b / a = -1/4
=> b = -a/4
=> √[(a - 0)² + (-a/4 - 0)²] = √(17a²/16)
From (a,-a/4) to (85,0), the distance is:
=> √[(85 - a)² + (0 - (-a/4))²] = √[(85 - a)² + (a/4)²]
These two separations are equal, so we can put them at the same value and find a:
=> √[(85 - a)² + (a/4)²] = √(17a²/16)
When we square both edges, we obtain:
=> (85 - a)² + (a/4)² = 17a²/16
=> 16(85 - a)² + a² = 17a²
=> 16(7225 - 170a + a²) + a² = 17a²
=> 115600 - 2720a + 17a² + a² = 17a²
=> 18a² - 2720a + 115600 = 0
=> 9a² - 1360a + 57800 = 0
=> a = (1360 ± √(1360² - 4957800)) / (2*9)
=> a = (1360 ± √(307600)) / 18
=> a = (1360 ± 560) / 18
=> a = 80 or a = 40/9
Point A's y-coordinate is:
=> b = -a/4 = -80/4 = -20
Consequently, spot A's coordinates are (80,-20).
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HELP
Recipe:
Cinnamom Rolls
makes 12 rolls
1/4 -ounce package active dry yeasy
1 cupt warm water
3 tablespoons molasses
1/3 cup powedered milk
1 egg yolk,beaten
1 egg white, beaten
3 1/2 cups bread flour, divided
6 tablespoons butter, melted and divided
1 teaspoon salt
1/2 cup whole wheat flour
1/3 cup raisins
1 large egg, beaten
1/4 cup water
You will use the recipe above to answer the following questions:
Respond to the questions about the second recipe:
This recipe makes 12 rolls, but you need to make 30 rolls. What number will you need to multiply the amount of each ingredient by to adjust the recipe? How did you determine this number?
How many ounces of yeast will you need to make 30 rolls?
How many cups of powdered milk will you need to make 30 rolls?
How many tablespoons of butter will you need to make 30 rolls?
How many more cups of bread flour than whole wheat flour will you need to make 30 rolls?
Notice that the original recipe calls for
1
4
cup of water. If you put in
3
8
cup of water, by how much have you
Answers
To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.
What is factor?A factor is a number or expression that divides another number or expression evenly without a remainder.
According to question:To adjust the recipe to make 30 rolls instead of 12, we need to multiply the amount of each ingredient by a factor of 30/12 = 2.5.
To determine this factor, we divide the desired number of rolls (30) by the original number of rolls (12):
2.5 = 30/12
To find the amounts of each ingredient needed to make 30 rolls, we multiply the original amounts by 2.5:
Yeast: 1/4 oz x 2.5 = 0.625 oz (or about 0.63 oz)
Warm water: 1 cup x 2.5 = 2.5 cups
Molasses: 3 tbsp x 2.5 = 7.5 tbsp (or about 1/2 cup + 1 tbsp)
Powdered milk: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)
Egg yolk: 1 beaten yolk x 2.5 = 2.5 beaten yolks (or about 2 yolks)
Egg white: 1 beaten white x 2.5 = 2.5 beaten whites (or about 2 whites)
Bread flour: 3 1/2 cups x 2.5 = 8.75 cups (or about 8 3/4 cups)
Butter: 6 tbsp x 2.5 = 15 tbsp (or about 1 cup - 1 tbsp)
Salt: 1 tsp x 2.5 = 2.5 tsp (or about 2 1/2 tsp)
Whole wheat flour: 1/2 cup x 2.5 = 1.25 cups (or about 1 1/4 cups)
Raisins: 1/3 cup x 2.5 = 0.83 cups (or about 3/4 cup + 1 tbsp)
To make 30 rolls, you will need 0.625 oz (or about 0.63 oz) of yeast.
To make 30 rolls, you will need 0.83 cups (or about 3/4 cup + 1 tbsp) of powdered milk.
To make 30 rolls, you will need 15 tbsp (or about 1 cup - 1 tbsp) of butter.
To make 30 rolls, you will need 8.75 cups (or about 8 3/4 cups) of bread flour, which is 8.75 - 1.25 = 7.5 cups more than the 1.25 cups of whole wheat flour needed.
If you put in 3/8 cup of water instead of the 1/4 cup called for in the original recipe, you have added an extra 3/8 - 1/4 = 1/8 cup of water, or 2 tablespoons of water.
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Question 1
Find the unpaid balance, new interest, and purchasing power on the credit card after the minimum monthly payment is made. The interest charge for unpaid balances is 18% per year.
Credit Card Balance = $5000
Credit Limit = $5000
Minimum Payment = $125.00
Answers
After making the minimum payment of $125, the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.
How to find the purchasing power?If the minimum monthly payment of $125 is made, we can calculate the new balance, unpaid balance, and interest charge as follows:
The interest rate per month is (18% per year) / 12 = 1.5% per month.
First, we calculate the interest charge for the month on the unpaid balance:
Interest charge = (1.5% per month) x ($5000 unpaid balance)
Interest charge = $75
Next, we subtract the minimum payment from the unpaid balance to get the new unpaid balance:
Unpaid balance = $5000 - $125
Unpaid balance= $4875
Then, we add the interest charge to the new unpaid balance to get the new balance:
New balance = $4875 + $75
New balance = $4950
Finally, we can calculate the purchasing power as the credit limit minus the new balance:
Purchasing power = $5000 - $4950
Purchasing power = $50
Therefore the unpaid balance on the credit card is $4875, the new interest charge is $75, and the purchasing power is $50.
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